Second-order properties and central limit theorems for geometric functionals of Boolean models

DOI10.1214/14-AAP1086zbMath1348.60013arXiv1308.6519MaRDI QIDQ259568

Daniel Hug, Matthias Schulte, Günter Last

Publication date: 11 March 2016

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.6519

zbMATH Keywords

Malliavin calculuscovariance matrixcentral limit theoremintegral geometryadditive functionalintrinsic volumeBoolean modelcurvature measureBerry-Esseen boundFock space representationWiener-Itō chaos expansion

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Stochastic calculus of variations and the Malliavin calculus (60H07) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (26)

Second Order Analysis of Geometric Functionals of Boolean Models ⋮ Local tensor valuations ⋮ Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds ⋮ Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes ⋮ A central limit theorem for Lipschitz-Killing curvatures of Gaussian excursions ⋮ Leaves on the line and in the plane ⋮ The Malliavin–Stein Method on the Poisson Space ⋮ Introduction to Stochastic Geometry ⋮ Rates of multivariate normal approximation for statistics in geometric probability ⋮ Vector-valued statistics of binomial processes: Berry-Esseen bounds in the convex distance ⋮ The Widom -- Rowlinson model under spin flip: immediate loss and sharp recovery of quasilocality ⋮ Lipschitz-Killing curvatures of excursion sets for two-dimensional random fields ⋮ Asymptotic behavior of mean density estimators based on a single observation: the Boolean model case ⋮ Anisotropy in finite continuum percolation: threshold estimation by Minkowski functionals ⋮ On approximation theorems for the Euler characteristic with applications to the bootstrap ⋮ The random connection model and functions of edge-marked Poisson processes: second order properties and normal approximation ⋮ Random geometric complexes in the thermodynamic regime ⋮ Concentration inequalities for functionals of Poisson cylinder processes ⋮ Multivariate second order Poincaré inequalities for Poisson functionals ⋮ Concentration inequalities for measures of a Boolean model ⋮ On the law of the iterated logarithm and strong invariance principles in stochastic geometry ⋮ Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization ⋮ Limit theorems for distributions invariant under groups of transformations ⋮ Functional limit theorems for the euler characteristic process in the critical regime ⋮ Second-order properties and central limit theorems for geometric functionals of Boolean models ⋮ Limit theory for the Gilbert graph

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